Average Error: 0.0 → 0.0
Time: 623.0ms
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(x, y, z \cdot t\right)
double f(double x, double y, double z, double t) {
        double r151472 = x;
        double r151473 = y;
        double r151474 = r151472 * r151473;
        double r151475 = z;
        double r151476 = t;
        double r151477 = r151475 * r151476;
        double r151478 = r151474 + r151477;
        return r151478;
}
↓
double f(double x, double y, double z, double t) {
        double r151479 = x;
        double r151480 = y;
        double r151481 = z;
        double r151482 = t;
        double r151483 = r151481 * r151482;
        double r151484 = fma(r151479, r151480, r151483);
        return r151484;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, z \cdot t\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))